World Football Elo Ratings

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The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.[2]

Top 60 ranking[edit]

The following table shows World Football Elo Ratings on 4 August 2016, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Rankings are shown as they were on 11 August 2016.[4]

AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA

Highest average ratings since 1970[edit]

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 August 2016. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.

Rank Country Avg Elo
1  Brazil 2013.1
2  Germany[a] 1981.8
3  Netherlands 1926.9
4  England 1922.1
5  Italy 1920.5
6  Spain 1912.9
7  Argentina 1909.2
8  France 1883.9
9  Russia[b] 1848.0
10  Czech Republic[c] 1828.2
11  Portugal 1821.1
12  Serbia[d] 1812.4
13  Sweden 1797.6
14  Mexico 1779.8
15  Romania 1779.0
16  Uruguay 1778.1
17  Poland 1770.0
Rank Country Avg Elo
18  Belgium 1767.5
19  Denmark 1757.0
20  Scotland 1736.4
21  Chile 1728.4
22  Paraguay 1725.2
23  Republic of Ireland 1720.8
24  Bulgaria 1701.9
25  Australia 1700.4
26  Colombia 1696.8
27   Switzerland 1691.5
28  Austria 1690.2
29  Hungary 1683.8
30  Iran 1676.9
31  South Korea 1668.4
32  Greece 1655.9
33  Nigeria 1654.5
34  Egypt 1654.2
Rank Country Avg Elo
35  Wales 1652.7
36  Peru 1649.1
37  Ivory Coast 1642.9
38  Israel 1642.1
39  Morocco 1640.2
40  Turkey 1639.0
41  Cameroon 1636.6
42  Norway 1635.8
43  Ghana 1615.1
44  United States 1613.3
45  Costa Rica 1606.2
46  Northern Ireland 1603.2
47  Tunisia 1601.4
48  Japan 1598.0
49  Ecuador 1594.5
50  Iraq 1590.0
51  Algeria 1574.6

List of number one teams[edit]

The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:

Ranking by days as leader[edit]

Nation days First Date as Leader Last Date as Leader
 England 11,231 30 November 1872 11 June 1988
 Argentina 8,218 1 November 1929 Current
 Brazil 8,104 12 June 1958 7 July 2014
 Scotland 5,864 4 March 1876 11 March 1904
 Germany [e] 4,284 25 July 1966 28 May 2016
 Italy 2,713 6 June 1934 14 August 2006
 Spain 2,495 5 September 1920 11 October 2013
 Uruguay 2,419 25 July 1920 8 July 1931
 Denmark 1,996 4 April 1914 20 September 1919
 France 1,856 12 September 1984 9 July 2007
 Hungary 1,289 25 November 1953 11 June 1958
 Russia [f] 1,097 31 March 1963 24 June 1988
 Netherlands 921 5 April 1920 3 July 2014
 Austria 10 27 May 1934 5 June 1934
 Czech Republic 8 27 June 2004 7 June 2005
 Poland 4 11 October 1975 14 October 1975

Elo all-time records[edit]

All-time highest ratings[edit]

The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.

All-time highest ranking[edit]

The following is a list of national football teams ranked by their highest Elo ranking ever reached.

Averages by decade[edit]

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).

Rank 1920s 1930s 1940s [n] 1950s 1960s
1 1911

 Uruguay

1976

 Argentina

2036

 Argentina

2025

 Argentina

1962

 Brazil

2 1873

 Spain

1970

 Italy

2018

 Italy

1998

 Hungary

1928

 England

3 1859

 Argentina

1899

 Uruguay

1892

 England

1996

 Brazil

1924

 Hungary

4 1843

 Scotland

1868

 Spain

1876

 Brazil

1917

 England

1923

 Argentina

5 1820

 Czechoslovakia

1867

 England

1858

 Spain

1870

 West Germany

1918

 Soviet Union

6 1795

 Denmark

1859

 Austria

1852

 Uruguay

1856

 Uruguay

1887

 West Germany

7 1771

 Brazil

1841

 Scotland

1841

 Scotland

1853

 Italy

1867

 Czechoslovakia

8 1768

 England

1814

 Czechoslovakia

1832

 Germany

1850

 Yugoslavia

1852

 Italy

9 1761

 Hungary

1810

 Brazil

1815

 Hungary

1817

 Austria

1844

 Spain

10 1760

 Austria

1785

 Hungary

1783

 Mexico

1815

 Spain

1840

 Uruguay

11 1739

 Netherlands

1767

 Costa Rica

1768

 Czechoslovakia

1799

 Paraguay

1811

 Yugoslavia

12 1712

 Sweden

1759

 Germany

1766

 Austria

1796

 Sweden

1801

 Scotland

13 1701

 Belgium

1685

 Denmark

1746

 Wales

1791

 Scotland

1796

 Sweden

14 1693

 Italy

1682

 Sweden

1734

 Sweden

1753

 France

1783

 Mexico

15 1676

 Portugal

1678

 United States

1719

 Paraguay

1728

 Peru

1741

 Austria

Rank 1970s 1980s 1990s 2000s 2010s [o]
1 2060

 Brazil

1975

 Brazil

1999

 Brazil

1998

 Brazil

2055

 Spain

2 2041

 West Germany

1964

 West Germany

1988

 Germany

1984

 France

2047

 Germany

3 1948

 England

1951

 Soviet Union

1952

 Italy

1966

 Netherlands

2044

 Brazil

4 1933

 Italy

1927

 England

1928

 France

1964

 Argentina

2001

 Netherlands

5 1888

 Netherlands

1897

 Argentina

1920

 Netherlands

1955

 Spain

1979

 Argentina

6 1884

 Poland

1890

 Italy

1904

 Spain

1942

 Italy

1916

 England

7 1878

 Soviet Union

1884

 Netherlands

1902

 FR Yugoslavia[p]

1916

 England

1888

 Chile

8 1869

 East Germany

1884

 France

1901

 England

1891

 Germany

1883

 Uruguay

9 1861

 Argentina

1847

 Spain

1874

 Denmark

1887

 Portugal

1879

 Portugal

10 1851

 Spain

1840

 Poland

1869

 Argentina

1873

 Czech Republic

1867

 Italy

11 1838

 Czechoslovakia

1820

 Czechoslovakia

1843

 Czech Republic[q]

1838

 Croatia

1861

 France

12 1831

 Hungary

1819

 Belgium

1836

 Sweden

1825

 Mexico

1860

 Colombia

13 1830

 Yugoslavia

1818

 Yugoslavia

1829

 Croatia

1822

 Denmark

1854

 Mexico

14 1809

 Scotland

1803

 East Germany

1826

 Russia[r]

1808

 Sweden

1833

 Croatia

15 1803

 Portugal

1785

 Uruguay

1825

 Mexico

1800

 Romania

1796

 Sweden

16 1793

 Belgium

1784

 Romania

1813

 Romania

1790

 United States

1794

 Russia

17 1771

 Sweden

1783

 Scotland

1810

 Portugal

1787

 Ireland

1787

 Ecuador

18 1767

 Austria

1776

 Sweden

1784

 Colombia

1786

 Turkey

1772

 Ivory Coast

19 1766

 Romania

1775

 Austria

1777

 Ireland

1782

 Uruguay

1769

 Switzerland

20 1755

 France

1774

 Denmark

1773

 Belgium

1774

 Australia

1767

 Ukraine

Highest rated matches[edit]

A list of the 16 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4240  Germany 2180  Argentina 2060 1 : 0 aet 2014-07-13 World Cup F Brazil Rio de Janeiro
 Germany 2200  Argentina 2040 2 : 4 2014-09-03 Friendly[9] Germany Düsseldorf
3 4213  Netherlands 2101  Spain 2112 0 : 1 aet 2010-07-11 World Cup F South Africa Johannesburg
4 4198  Brazil 2100  Germany 2098 1 : 7 2014-07-08 World Cup SF Brazil Belo Horizonte
5 4192  Brazil 2064  Spain 2128 3 : 0 2013-06-30 Confederations Cup F Brazil Rio de Janeiro
6 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Switzerland Bern
7 4160  Netherlands 2051  Brazil 2109 2 : 1 2010-07-02 World Cup QF South Africa Port Elizabeth
8 4152  Brazil 2062  Netherlands 2090 0 : 0 2011-06-04 Friendly Brazil Goiânia
9 4150  West Germany 2069  Brazil 2081 0 : 1 1973-06-16 Friendly West Germany Berlin
10 4135  Netherlands 2075  Argentina 2060 0 : 0 2014-07-09 World Cup SF Brazil São Paulo
11 4130  Spain 2086  Germany 2044 1 : 0 2010-07-07 World Cup SF South Africa Durban
12 4121  Brazil 2051  West Germany 2070 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
13 4118  Hungary 2108  Brazil 2010 4 : 2 1954-06-27 World Cup QF Switzerland Bern
14 4116  Hungary 2141  Uruguay 1975 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
15 4114  West Germany 2080  Netherlands 2034 2 : 1 1974-07-07 World Cup F West Germany Munich
16 4113  Argentina 2098  Chile 2015 0 : 0 2016-06-26 Copa América F United States East Rutherford

Biggest upsets[edit]

A list of the 15 matches with the biggest point exchange.[s] Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[t] The nations' points before the matches are given.

Rank Point
exchange
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 95  Sweden 1621  Belgium 1772 8 : 1 1924-05-29 Olympic Games France Paris
2 85  Fiji 1148  New Zealand 1534 4 : 0 1980-02-23 OFC Nations Cup New Caledonia Nouméa
 Czechoslovakia 1809  Argentina 1964 6 : 1 1958-06-15 World Cup Sweden Helsingborg
4 84  Poland 1583  Hungary 1823 3 : 0 1936-08-05 Olympic Games Germany Berlin
5 82  Brazil 2100  Germany 2098 1 : 7 2014-07-08 World Cup Brazil Belo Horizonte
6 81  Ghana 1598  Czech Republic 1975 2 : 0 2006-06-17 World Cup Germany Cologne
7 80  Khmer Republic 1200  Kuwait 1510 4 : 0 1972-05-14 Asian Cup Thailand Bangkok
8 79  Paraguay 1596  Uruguay 1986 3 : 0 1929-11-01 Copa América Argentina Buenos Aires
9 78  Croatia 1873  Germany 2054 3 : 0 1998-07-04 World Cup France Lyon
 Norway 1535  Great Britain 1865 3 : 1 1920-08-28 Olympic Games Belgium Antwerp
11 77  Uruguay 1785  Brazil 2125 3 : 0 1959-12-12 Copa América Ecuador Guayaquil
 Chile 1540  Uruguay 1893 3 : 0 1937-01-10 Copa América Argentina Buenos Aires
13 76  Netherlands 1962  Spain 2088 5 : 1 2014-06-13 World Cup Brazil Salvador
 United States 1869  Mexico 1772 0 : 5 2009-07-26 CONCACAF Gold Cup United States East Rutherford
 Germany 1851  Norway 1650 0 : 2 1936-08-07 Olympic Games Germany Berlin

History[edit]

The Elo system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

Overview[edit]

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

  • The team's old rating
  • The considered weight of the tournament
  • The goal difference of the match
  • The result of the match
  • The expected result of the match

The different weights of competitions in descending order are:

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.

Basic calculation principles[edit]

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings change are based on the following formulae:

or

Where;

= The new team rating
= The old team rating
= Weight index regarding the tournament of the match
= A number from the index of goal differences
= The result of the match
= The expected result
= Points Change

The number of Points Change is rounded to the nearest integer before updating the team rating.

Status of match[edit]

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup 60
Continental Championship and Intercontinental Tournaments 50
World Cup and Continental qualifiers and major tournaments 40
All other tournaments 30
Friendly Matches 20

Number of goals[edit]

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is a draw or is won by one goal

If the game is won by two goals

If the game is won by three or more goals

  • Where N is the goal difference

Table of examples:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

Result of match[edit]

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

Expected result of match[edit]

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

where dr equals the difference in ratings (add 100 points for the home team). So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

Examples[edit]

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

Example 1[edit]

Team A versus Team B (Team A stronger than Team B)

Team A Team B Team A Team B Team A Team B
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.679 0.321 0.679 0.321 0.679 0.321
Total (P) +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

Example 2[edit]

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

Team B Team C Team B Team C Team B Team C
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.529 0.471 0.529 0.471 0.529 0.471
Total (P) +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

See also[edit]

Notes[edit]

  1. ^ Representing West Germany from 1949 to 1990
  2. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  3. ^ Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
  4. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
  5. ^ Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
  6. ^ Combined record of the Russian Empire (1912-1914), RSFSR (1923), USSR (1924-1992), CIS (1992), and Russia (1992-present) national football teams.[8]
  7. ^ as Soviet Union
  8. ^ as FR of Yugoslavia
  9. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  10. ^ as Zaire
  11. ^ as Soviet Union
  12. ^ as FR of Yugoslavia
  13. ^ as Zaire
  14. ^ In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
  15. ^ up to 1 August 2016
  16. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
  17. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
  18. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
  19. ^ Only matches between teams with at least 30 earlier matches each are included to allow a stabilized Elo rating. These criteria just disqualify the 4:0 Turkey:China match at the 1948 Olympic Games and the 7:1 Italy:Spain match at the 1928 Olympic Games, each with an 89 point exchange,[10] the 3:0 Egypt:Hungary at the 1924 Olympic Games with a 80 point exchange,[11] the 4:2 Peru:Austria at the 1936 Olympic Games with a 78 point exchange,[12] and the 4:1 France:Mexico at the 1930 World Cup with a 76 point exchange.[13]
  20. ^ In those terms, Luxembourg featured in the two most surprising wins. First the 2:1 win over Switzerland (ER 1767) in a World Cup qualification match in September 2008 (a 762 point difference), followed by the 1:0 win vs. Czech Republic (ER 1854) in a EURO qualification match in June 1995 (a 702 point difference).[14] These are the only wins for a team with at least 700 points less than its opponent.

References[edit]

  1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012. 
  2. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  3. ^ World Football Elo Ratings Eloratings.net. Retrieved: 2016-08-04.
  4. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 11 August 2016. Retrieved 2016-08-11. 
  5. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  6. ^ Arpad Elo, Chess Life, 1962.
  7. ^ About the Chessmetrics Rating System, by Jeff Sonas
  8. ^ "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04. 
  9. ^ "Germany to play Argentina in September friendly". The Star. 21 March 2014. Retrieved 15 July 2014. 
  10. ^ Source: World Football Elo Ratings: Biggest Upsets
  11. ^ Source: World Football Elo Ratings: Egypt
  12. ^ Source: World Football Elo Ratings: Peru
  13. ^ Source: World Football Elo Ratings: Mexico
  14. ^ Source: World Football Elo Ratings: Luxembourg

External links[edit]